A rectangle is 19 feet long and 42 feet wide. What is the area of the rectangle, in square yards? Express your answer as a mixed number in lowest terms.

Answer:

Total number of students= 7+ 9+4+5= 25

Tennis: total= 5:25= 1:5 (simplify by dividing both sides by 5

Answer:

1:5

Step-by-step explanation:

First We Add The Number Of Students.

7+9+4+5=25

the students were divided into 5 kind of sports so it will be 5/25

5/25 means 1/5 and

1/5 means 1:5

The expression which is equivalent to the given expression; 2(3a+2b−7) is; 6a +4b -14

The given expression is;

Upon expansion by multiplying all elements in the parenthesis by 2; we have;

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Final answer:

By distributing the 2 across each term in the expression 2(3a+2b-7), the equivalent expression is 6a + 4b - 14, which corresponds to answer choice D.

Explanation:

To determine which expression is equivalent to 2(3a+2b-7), we need to distribute the 2 across each term in the parentheses. This means we'll multiply 2 by 3a, 2b, and -7 separately. Here's the step-by-step distribution:

Combining these results, we get the equivalent expression: 6a + 4b - 14, which matches answer choice D.

Answer:

the answer is A)

Step-by-step explanation:

-11 + 15 = 4

4 - 8 = -4

-4 + 4 = 0

Answer:

Step-by-step explanation:

Hello

The temperature rises 15 degrees Fahrenheit (ﾟF) and then drops by 8ﾟF. If the temperature started at -11ﾟF, what temperature change would be required to bring the temperature to 0ﾟF?

A) an Incase of 4ﾟF

B) a decreased of 4ﾟF

C) a decreased of 19ﾟF

D) an increase of 19ﾟF

-11 + 15 - 8 = -19 + 15 = -4° F

A) An increase of 4° F

Answer:

x=1

Step-by-step explanation:

use distributive property for the negative 5, then simplify, then bring the 15 to the other side, then divide by 3. picture included.

Answer:

[tex]\large\boxed{y=\dfrac{7}{2}x-2}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the point (4, 12), and y-intercept b = -2 → (0, -2).

Substitute:

[tex]m=\dfrac{-2-12}{0-4}=\dfrac{-14}{-4}=\dfrac{14:2}{4:2}=\dfrac{7}{2}[/tex]

Finally:

[tex]y=\dfrac{7}{2}x-2[/tex]

Answer:

x = 4 ± [tex]\sqrt{19}[/tex]

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{19}[/tex], that is

x = 4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex]

Final answer:

The solution set for the quadratic equation x² - 8x = 3 is found by completing the square, resulting in (4 - √19, 4 + √19).

Explanation:

To solve the quadratic equation by completing the square, we start with x² – 8x = 3. First, we move the constant term to the other side of the equation:

x² – 8x + ____ = 3 + ____

Now we need to find a number to fill in the blanks that makes the left side a perfect square trinomial. To do this, take half of the coefficient of x, which is -8/2 = -4, and then square it, which gives us 16. Add 16 to both sides:

x² – 8x + 16 = 3 + 16

x² – 8x + 16 = 19

The left side is now a perfect square, (x – 4)² = 19. Taking the square root of both sides gives us:

x – 4 = ±√19

Add 4 to both sides to solve for x:

x = 4 ±√19

Therefore, the solution set for the equation x² – 8x = 3 is (4 – √19, 4 + √19).

Answer:

(8,-3)

Step-by-step explanation:

(x1+x2/2), (y1+y2/2)

7+9/2=16/2=8           x=8

-5-1/2=-6/2=-3          y=-3

Answer:

Step-by-step explanation:

The formula of a midpoint of AB

[tex]A(x_A,\ y_A),\ B(x_B,\ y_B)\\\\M_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)[/tex]

We have the points X(7, -5) and Y(9, -1).

Substitute:

[tex]M_{XY}\left(\dfrac{7+9}{2};\ \dfrac{-5+(-1)}{2}\right)\\\\M_{XY}\left(\dfrac{16}{2};\ \dfrac{-6}{2}\right)\\\\M_{XY}(8,\ -3)[/tex]

Answer:

1/2

Step-by-step explanation:

both have equal chances

The required probabilities are 3/8 and 1/8 respectively.

Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

Given here: Jackie has 6 skirts and 2 dresses.

Total number of dresses=8

Thus the probability of picking a skirt is = 6/8

                                                                   =3/4

And the probability of picking a dress is =2/8

                                                             =1/4

Also, the probability of choosing either shoe is 1/2

Therefore the conditional probability that she chooses a skirt and brown shoes is = 3/4×1/2

              =3/8

Similarly Probability( dress+black shoes)=1/4×1/2

                                                                   =1/8

Hence, The required probabilities are 3/8 and 1/8 respectively.

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Answer:

The value of product is 7.

Step-by-step explanation:

Since we have given that

4 square 7x4 square root 7x4 square root 7x4 square root 7

We need to find the product of the following terms:

We will apply the "law of exponents":

i.e.

(a^m)^n=a^{mn}

4 square 7x4 square root 7x4 square root 7x4 square root 7

=7 ^(1/4)4=7

Hence, the value of product is 7.

The value of product is 7.

The term "product" refers to the result of one or more multiplications. For example, the mathematical statement would be read " times equals ," where is called the multiplier, the multiplicand and is their product.

Given is an expression, 4 square 7 • 4 square root 7• 4 square root 7 •4 square root 7

Converting into mathematical notation,

= [tex]\sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} .[/tex]

We need to find the product of the following terms:

We will apply the "law of exponents":

(xᵃ)ᵇ = xᵃᵇ

[tex](\sqrt[4]{7})^4\\\\= (7^\frac{1}{4})^4\\\\= 7[/tex]

Hence, the value of product is 7.

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The answer is 254.47 ft

Step-by-step explanation:

V=pi×r^2×h

pi=3.14

r=d/2

r=6/2=3

v=(3.14)×3^2×9

=254.47 ft

Answer:

54ft

Step-by-step explanation:

The formula for volume is base *height

[tex]\bf \begin{array}{ccll} inches&cents\\ \cline{1-2} 17&51\\ 33&x \end{array}\implies \cfrac{17}{33}=\cfrac{51}{x}\implies 17x=33\cdot 51\implies x = \cfrac{33\cdot 51}{17} \\\\\\ x = 33\cdot \cfrac{51}{17}\implies x = 33\cdot 3\implies x = 99[/tex]

Final answer:

To find the cost of 33 inches of wire, we calculate the cost per inch from the given 17 inches costing 51 cents, which is 3 cents per inch, and then multiply by 33 inches to get a total cost of 99 cents.

Explanation:

The student is asking to determine the cost of 33 inches of wire based on the given rate of 17 inches costing 51 cents. To solve this, we can set up a proportion where we compare the given inches of wire to the given cost and then find the cost for the desired inches of wire.

Step-by-Step Calculation:

First, we determine the cost per inch of wire by dividing the total cost by the total length of wire: 51 cents ÷ 17 inches = 3 cents per inch.

Next, we multiply the cost per inch by the desired length of wire to find the total cost: 3 cents/inch × 33 inches = 99 cents.

Therefore, 33 inches of wire will cost 99 cents at the same rate.

Answer:

y = - [tex]\frac{1}{6}[/tex] x - [tex]\frac{8}{9}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Rearrange 3x + 18y = - 16 into this form

Subtract 3x from both sides

18y = - 3x - 16 ( divide all terms by 18 )

y = - [tex]\frac{3}{18}[/tex] x - [tex]\frac{16}{18}[/tex], that is

y = - [tex]\frac{1}{6}[/tex] x - [tex]\frac{8}{9}[/tex] ← in slope- intercept form

Answer:

1/1000 or 1x10^(-3)

Step-by-step explanation:

0.001=1/1000 as a fraction

With a negative exponent?

You can write it into standard notation.

It's 1x10^(-3).

0.001 as a fraction with a negative exponent is 10⁻³.

To express the decimal 0.001 as a fraction with a negative exponent, we need to understand how negative exponents work with powers of ten. The decimal 0.001 is equivalent to the fraction [tex]\frac{1}{1000}[/tex], which can be written as [tex]\frac{1}{103}[/tex].

Using the concept of negative exponents, [tex]\frac{1}{103}[/tex] can be rewritten as 10⁻³. This is because a negative exponent indicates the inverse of the corresponding positive exponent. So, 0.001 = 10⁻³.

Summary in Steps:

Therefore, 0.001 equals 10⁻³ as a fraction with a negative exponent.

Answer:

k = 5 and (6,2).

Step-by-step explanation:

Since (1,-1) is a solution of the equation 3x - ky = 8, so the point (1,-1) will satisfy the equation above.

Hence, putting x = 1 and y = -1 in the equation will give left-hand side = right-hand side.

So, 3(1) - k(-1) = 8

⇒ 3 + k = 8

⇒ k = 5 (Answer)

Therefore, the equation of the straight line is 3x - 5y = 8 ....... (1)

Now, putting x = 6 , then from equation (1) we get y = 2

Therefore, (6,2) is also a point on the graph of equation (1). (Answer)

Answer:

f(x)=5-x

Step-by-step explanation:

The equation y + x = 5 in function notation is f(x) = 5 - x, done by isolating the dependent variable, y, and expressing it as a function of x.

The equation y + x = 5 can be rewritten in function notation by isolating the dependent variable, y, which is standard procedure in function notation. To isolate y, we need to subtract x from both sides of the equation. Thus, the equation y + x = 5 becomes y = 5 - x. In function notation, where y is typically written as f(x), this would become f(x) = 5 - x.

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Answer:

Answer:

213

Step-by-step explanation:

Let

The relationship between x and y can be represented through a linear equation.

y = a . x + b

where,

a is the slope

b is the y-intercept

The slope refers to the price per print, that is, a = $0.15/p.

Then,

y = $0.15/p . x + b

Even if x = 0, there is a fixed cost of $3.00 (y = $3.00). We can replace these values in the expression above.

$3.00 = $0.15/p . 0 + b

b = $3.00

The final equation is:

y = $0.15/p . x + $3.00

If MaryAnn has $35,

$35 = $0.15/p . x + $3.00

$32 = $0.15/p . x

x = 213 p

She can order 213 prints.

The expression to determine the total amount Joe spent on gasoline and oil is 2.85 * g + 3.15 * c. If Joe bought 8.4 gallons of gasoline and 6 cans of oil, he will have spent 42.84 dollars in total.

Part A: To determine the total amount Joe spent on gasoline and oil, we need to calculate the cost of gasoline and the cost of oil separately, and then add them together.

The expression to calculate the cost of gasoline is: 2.85 * g, where 'g' represents the number of gallons of gasoline Joe bought.

The expression to calculate the cost of oil is: 3.15 * c, where 'c' represents the number of cans of oil Joe bought.

Therefore, the expression to determine the total amount Joe spent is: 2.85 * g + 3.15 * c.

Part B: If Joe bought 8.4 gallons of gasoline and 6 cans of oil, we can substitute these values into the expression we derived in Part A.

The total amount Joe spent can be calculated as follows:

Total amount spent = 2.85 * 8.4 + 3.15 * 6

Simplifying the expression:

Total amount spent = 23.94 + 18.90

Total amount spent = 42.84 dollars

Answer:

fifteen

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

1/4(60)=60/4=15

Answer:

The distance between A and B is l(AB) = 13 units

Step-by-step explanation:

Given:

let,

A ≡ ( x1, y1 ) ≡ ( 0, 12 )

B ≡ ( x2, y2 ) ≡ ( 5, 0 )

To Find:

Length AB = ?

Solution:

Distance Formula for the distance between the two points ( x1, y1 ) and ( x2, y2 ) we have,

[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]

On substituting the above values we will get,

[tex]l(AB) = \sqrt{((5-0)^{2}+(0-12)^{2} )}\\l(AB)=\sqrt{(5^{2} +(-12)^{2} } \\l(AB)=\sqrt{(25+144)}\\ l(AB)=\sqrt{169} \\l(AB)=13\ unit[/tex]

Therefore the distance between A and B is l(AB) = 13 units

Step-by-step explanation:

When you divide fractions, you multiply by the reciprocal.

The new equation would be:

[tex] \frac{5}{\frac{3}{8} \times \frac{8}{7} } [/tex]

[tex] \frac{5}{1} \times \frac{7}{3} = \frac{35}{3} [/tex]

Answer:

200/21

Step-by-step explanation:

5/(3/5) divided by 7/8

First divide 5 by 3/5. To do this you must write 5 as 5/1, and multiply 5/1 by the reciprocal of 3/5 (5/3).

5/1 (5/3)

numerator: 5*5=25

denominator: 1*3=3

25/3

Then divide 25/3 by 7/8 by multiplying 25/3 by the reciprocal of 7/8 (8/7).

25/3 (8/7)

numerator: 25*8= 200

denominator: 3*7= 21

200/21 or 9 11/21

Answer:

x = -2

y = 4

Step-by-step explanation:

Given

[tex]-10x+12i=20+3yi[/tex]

Two complex numbers are equal when they have equal real and imaginary parts.

Equate real parts:

[tex]-10x=20\\ \\x=-\dfrac{20}{10}=-2[/tex]

Equate imaginary parts:

[tex]12=3y\\ \\y=\dfrac{12}{3}=4[/tex]

Final answer:

The values of x and y that satisfy the given complex equation are x = -2 and y = 4, found by equating the real and imaginary parts respectively.

Explanation:

To find the values of x and y that satisfy the equation -10x + 12i = 20 + 3yi, we need to equate the real parts and the imaginary parts of the complex numbers on both sides of the equation.

For the real parts, we have:
-10x = 20
=> x = -2

For the imaginary parts, we have:
12 = 3y
=> y = 4

So the solution for the equation is x = -2 and y = 4.

A car is worth $300

Step-by-step explanation:

A board game allows players to trade and sell game pieces of equal value

We need to find how much the car is worth

Assume that the car is worth $x and the house is worth $y

∵ Player 1 traded three cars plus $100 for a house

∴ 3 x + 100 = y

- Subtract 100 from both sides

∴ 3 x = y - 100

- Subtract y from both sides

∴ 3 x - y = - 100 ⇒ (1)

∵ Player 2 sold two houses and a car for $2300

∴ x + 2 y = 2300 ⇒ (2)

Now we have system of equation to solve it

Multiply equation (1) by 2 to eliminate y

∵ 6 x - 2 y = - 200 ⇒ (3)

- Add equations (2) and (3)

∴ 7 x = 2100

- Divide both sides by 7

∴ x = 300

A car is worth $300

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We are testing the claim that males speak fewer words than females. With a p-value of 0.369, which is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, no significant evidence supports the claim that males speak fewer words than females.

The objective here is to test the claim that on average, males speak fewer words in a day than females. To do this, we compare two means using a hypothesis test for paired data.

The null hypothesis (H0) is that there is no difference between the mean number of words spoken by males and females. The alternative hypothesis (Ha) is that the mean number of words spoken by males is less than that spoken by females.

Since the p-value (0.369) is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means we do not have significant evidence to support the claim that males speak fewer words than females.

A key takeaway from this is that the test statistic and p-value are critical elements in hypothesis testing. They determine whether or not you have significant evidence to reject the null hypothesis.

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The real is B.) f(x) = -x + 11

A.) f(x) = -y + 11 is the wrong answer.

I have pictures to prove that they are the same in the graph as x + y = 11.

Hope this will help a lot more than the other answer.

Answer:

B.) f(x) = -x + 11

Step-by-step explanation:

Helen uses 0.3 kg of nuts for 2.5 kg of granola.

Multiplication is an operation that represents the basic idea of repeated addition of the same number.

Given that, Helen uses 0.12 kilogram of nuts in each batch of granola

that she makes, and she makes 2.5 batches,

For 1 batch she uses .12 kg of nuts, so for 2.5 kg she will use = 2.5*0.12 = 0.3 kg

Hence, Helen uses 0.3 kg of nuts for 2.5 kg of granola.

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4. 3x + 2y = 6

x-intercept = 2 ,  y - intercept = 3

5. 4x – 9y = 36

x-intercept = 9, y - intercept = -4

6. x + y = -3

x-intercept = -3, y - intercept = -3

8. x - 3y = 12

x-intercept = 12, y - intercept = -4

Step-by-step explanation:

To find the x-intercept we put y=0 in the equation and to find the y-intercept we put x = 0 in the equation

4. 3x + 2y = 6

Putting y = 0

[tex]3x + 2y = 6\\3x +2(0) = 6\\3x = 6\\\frac{3x}{3} = \frac{6}{3}\\x= 2[/tex]

Putting x=0

[tex]3x + 2y = 6\\3(0) + 2y = 6\\2y = 6\\\frac{2y}{2} = \frac{6}{2}\\y= 3[/tex]

5. 4x – 9y = 36

Putting y = 0

[tex]4x -9y = 36\\4x - 9(0) = 36\\4x = 36\\\frac{4x}{4} = \frac{36}{4}\\x = 9[/tex]

Putting x=0

[tex]4(0) -9y = 36\\-9y=36\\\frac{-9x}{-9} = \frac{36}{-9}\\x =-4[/tex]

6. x + y = -3

Putting y = 0

[tex]x+y=-3\\x+0 = -3\\x = -3[/tex]

Putting x=0

[tex]x + y = -3\\0+y=-3\\y=-3[/tex]

8. X - 3y = 12

Putting y=0

[tex]x - 3(0) = 12\\x -0 = 12\\x = 12[/tex]

Putting x = 0

[tex]0-3y = 12\\-3y = 12\\\frac{-3y}{-3} =\frac{12}{-3}\\y=-4[/tex]

Keywords: Linear equation

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Answer:

[tex]\large\boxed{x^2+4x+3=(x+3)(x+1)}[/tex]

Step-by-step explanation:

[tex]x^2+4x+3\\\\\text{We are looking for a and b, for which a + b = 4 and (a)(b) = 3}\\\\\text{a=3,\ b=1}\\\\=x^2+3x+1x+3\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\=x\underbrace{(x+3)}_{(*)}+1\underbrace{(x+3)}_{(*)}\qquad\text{use the distributive property}\\\\=\underbrace{(x+3)}_{(*)}(x+1)[/tex]